Question

Please help me answer this question on congruent triangles. 30 points

Answer 1

h = 24 cm

Explanation:

Let
`x` = height of ΔCBD

Let
`h` = height of ΔABE

As ΔABE ~ ΔCBD then AE : CD =
`h` :
`x`

Given:

• AE = 20 cm
• CD = 10 cm

`\implies 20 : 10 = h : x`

`\implies (20)/(10)=(h)/(x)`

Cross multiply:

`\implies 20x=10h`

Simplify:

`\implies 2x=h`

As we are told that
`x+h=36 \ \sf cm`

`\implies h=36-x`

Equate the two equations for
`h` and solve for
`x`:

`\implies 2x=36-x`

`\implies 3x=36`

`\implies x=12`

Since
`h=2x` then

`\implies h=2 \cdot 12`

`\implies h=24 \ \sf cm`